Question: Simplify; express your answer in exponential form. Assume $q\neq 0, y\neq 0$. $\dfrac{{(q^{5})^{2}}}{{(q^{-5}y^{-2})^{4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${q^{5}}$ to the exponent ${2}$ . Now ${5 \times 2 = 10}$ , so ${(q^{5})^{2} = q^{10}}$ In the denominator, we can use the distributive property of exponents. ${(q^{-5}y^{-2})^{4} = (q^{-5})^{4}(y^{-2})^{4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q^{5})^{2}}}{{(q^{-5}y^{-2})^{4}}} = \dfrac{{q^{10}}}{{q^{-20}y^{-8}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{10}}}{{q^{-20}y^{-8}}} = \dfrac{{q^{10}}}{{q^{-20}}} \cdot \dfrac{{1}}{{y^{-8}}} = q^{{10} - {(-20)}} \cdot y^{- {(-8)}} = q^{30}y^{8}$.